DAMAGE PROGRESSION ANALYSIS OF COMPOSITE T-JOINTS
WITH TRANSVERSE REINFORCEMENT
Patrick B. Stickler and Mamidala Ramulu
Department of Mechanical Engineering
University of Washington
Seattle, WA 98195
ABSTRACT
A new type of T-joint with transverse reinforcement using a
fiber insertion process was analyzed using numerical
methods. T-joints modeled herein are fabricated from dry
fabric preforms using resin transfer molding. Fiber tows are
inserted into the dry fabric preforms prior to consolidation.
Experiments were conducted to determine the loaddisplacement and strain-load history under flexure loading.
A damage progression finite element model was developed
to predict the mechanical behavior under flexure loading
through ultimate failure. Experimental observations of initial
failure were marked by a discrete drop in the loaddisplacement behavior and the initiation and propagation of
an interfacial matrix crack at the web-to-flange interface.
Crack initiation is predicted under flexure loading when the
local matrix stress exceeds that of the neat resin tensile
strength in the fillet region of the T-joint. Fiber insertion
bridging and fiber insertion breakage were observed prior to
T-joint ultimate failure. The damage progression finite
element
analysis
showed
good
agreement
with
experimentally determined load-displacement values through
ultimate failure.
an iterative process to evaluate T-joints with viscoelastic
inserts [4].
In the present analysis, a T-joint with transverse stitching
was modeled through ultimate failure for the first time under
flexure loading. T-joints were modeled in a series of six
steps using a progressive damage FEA representing
accumulated damage through the entire load history.
2 EXPERIMENTAL OBSERVATIONS
A new one-sided stitching process, referred to as fiber
insertion, was developed as a low-cost method of joining
two-dimensional dry fiber preforms. Figure 1 shows the Tjoint configuration. Specimens are fabricated from T-300 dry
fabric preforms. Transverse stitching is accomplished using
IM7 6K fiber tow insertions and specimens are consolidated
using PR500 toughened epoxy resin and the RTM process.
4.75 mm
1 INTRODUCTION
Failure of composite materials with applied out-of-plane
loading tends to be matrix dominated. Flexure loading of Tjoints produces out-of-plane loading of the flange member.
The modeling of structures with transverse loading requires
consideration of material and geometric nonlinearities. Jones
and Alesi analyzed T-stiffeners with out-of-plane loading
using FEA [1] with material and geometric nonlinearities.
Experimental and numerical results showed good correlation
with the inclusion of nonlinear effects. Matrix dominated
failures in composite joints were also studied [2].
Progressive damage of composite T-joints was studied
extensively by Phillips and Shenoi [3]. In their study, it was
shown that T-joints fail in a series of steps with increasing
applied load. A progressive FEA was performed to model the
damage evolution through ultimate failure. T-joints were
shown to fail by delamination in the corner plies and matrix
cracking at the web-to-flange interface. Another study used
4.75 mm
12.7 mm
Web: T-300/PR520
Fabric [0/45] 6s
Transverse Stitching: IM7 6K Tow
Flange: T-300/PR520
Fabric [0/45] 6s
Figure 1: T-Joint configuration.
Extensive experimental investigations were performed on Tjoints constructed using the fiber-insertion process under
flexure, tensile, and shear loading [5-8]. In these
experiments, T-joints with transverse stitching failed in a
series of steps with increased load. Post failure analysis
revealed that damage initiated in the fillet region at the webto-flange interface. Increased load beyond initial failure
caused crack propagation in the fillet region and across the
web-to-flange interface. Additional loading caused fiber
insertion bridging; leading to ultimate T-joint failure via fiberinsertion breakage and pullout. T-joint flexure and tension
specimen web and flange members remained partially intact
through ultimate failure. Shear specimens failed with
complete separation of the web and flange. T-joints were
modeled up to initial failure using linear elastic finite element
analysis. Predicted and experimental results showed good
agreement in this load range. However, these investigations
did not included progressive damage analyses, representing
the entire load history. In the present analysis, T-joints are
modeled in a series of steps representing accumulated
damage through ultimate failure under flexural loading.
3 FINITE ELEMENT
ANALYSIS
MODELS
AND
METHOD
OF
A progressive damage analyses were performed on the Tjoint under flexure loading using ANSYS FEA software [9].
Two-dimensional finite element models were created using a
plane strain assumption. Plane strain was assumed in this
case because the specimen width is much greater than the
web or flange thickness. Fiber insertion tows were modeled
using simple beam elements. Damage progression was
modeled in a series of discrete steps representing an
accumulation of damage under increased load.
Table 1 shows the material properties used in the finite
element analysis. Vendor-supplied properties were used for
the Hexcel IM7 fiber insertions and 3M PR520 resin [10-11].
The experimentally determined elastic laminate properties,
as developed previously, were used for the T-300/PR520
quasi-isotropic web and flange [12].
Property
Ex (GPa)
Ey (GPa)
Ez (GPa)
νxy
νyz
νxz
Gxy (GPa)
Gyz (GPa)
Gxz (GPa)
Region 1
Insertion
276
276
276
0.30
0.30
0.30
106
106
106
Region 2
Interface
3.54
3.54
3.54
0.38
0.38
0.38
1.28
1.28
1.28
Region 3
Web
44.24
9.73
44.24
0.37
0.37
0.31
2.98
2.98
16.53
Region 4
Flange
9.73
44.24
44.24
0.37
0.31
0.37
2.98
16.53
2.98
TABLE 1: T-Joint Constituent Elastic Material Properties.
The IM7 6k fiber tow cross-sectional area, Atow was
determined using the following expression:
ATow = (
πd f 2
4
) * (# filaments)
3.1 Finite Element Model
The FEM, including fixed-support boundary conditions used
in the progressive damage FEA is shown in Figure 2. The
two rows of fiber insertions located in region 1 were modeled
using IM7 6k fiber insertion tow properties and 2-D spar
elements. Isotropic material properties were used for the
resin-rich fillet and web-to-flange interface region 2. The fillet
regions were modeled using 6-node triangular elements.
Quasi-isotropic material properties were used for composite
web and flange regions 3 and 4, respectively. The web and
flange were modeled using 8-node quadrilateral elements. A
nodal force was applied normal to the web 2.54 cm from the
web-to-flange interface. Fixed boundary conditions (zero
displacement) were assumed at the flange interface to
represent the bonded flange-to-fixture attachment constraint.
where df is the filament diameter [13]. There are 6000
filaments per 6k tow and 2 tows per fiber insertion. The IM7
fibers have a filament diameter of 5 µm and a fiber tow area
of 0.15 mm. The nominal circular tow diameter was
determined to be 0.50 mm, assuming a packing fraction of
0.75, where the packing factor is the area of fibers divided by
the area of a circle. The fiber insertion tow area and
diameter were used as input to the FEM element attributes.
In order to numerically model the T-joint, the resin-rich
interface zone thickness was required. Based on specimen
optical micrographs, the nominal resin-rich interface zone
thickness was determined to be 1.25 mm. This region was
assumed to be isotropic and was modeled using the PR520
neat resin properties. The variation and magnitude of the
interface thickness may be attributed to preform edge
roughness and fiber preform misalignment during T-joint
fabrication.
Region 4 - Flange
3.2 Damage Progression Criterion
Region 2 - Interface
Region 3 - Web
Region 1 - Insertion
Figure 2: FEA analysis regions and mesh.
A damage progression finite element analysis was
performed based on experimental observations and optical
micrographs of the failed flexure specimens as reported
previously [7]. These experiments demonstrated that a crack
initiates from the resin-rich fillet region and traverses the
web-to-flange interface under increased load. In order to
model this progressive damage, a series of six step FEMs
were created, representing an accumulation of damage with
increased load. In step 1 no damage is present, which
represents the elastic region of the load-displacement record
up to initial failure. Step 2 models an incipient crack in the
resin-rich fillet region at the web-to-flange interface. This
represents the initial drop in load displacement. The
magnitude of the drop is indicative of the extent of damage
to the T-joint. Step 3 models continued fillet crack
propagation, step 4 models the crack traversing the web-toflange interface, and step 5 models the crack extending to
the first fiber insertion. The first fiber insertion is the insertion
adjacent to the applied load. Step 6 models the crack
reaching the second fiber insertion. Figure 3 shows the finite
element mesh for the damage progression model step 6.
Crack initiation is predicted as the local matrix stress
exceeds that of the neat resin tensile strength in the fillet
region of the T-joint. As shown, the load-displacement plot is
then nearly linear from point “b” up to point “c”. In this
region, as indicated by the analysis, the crack is propagating
to the second fiber insertion and increasing the apparent
load on the first fiber insertion. From point “c” to point “d” in
Figure 4, the first fiber insertion is degrading. Further loading
beyond point “d" then results in fiber tow filament breakage
and insertion/matrix interface degradation.
Figure 5 shows the effective stress contour plots for damage
progression model step 6. As defined by the failure analysis,
damage progresses at the point when the peak effective
stress exceeds that of the PR520 neat resin tensile strength
in the radius fillet and web-to-flange interface regions. Step 6
shows the damage progressing beyond the fiber insertion
adjacent to the applied load, representing extensive
interfacial matrix cracking and fiber insertion bridging at the
web-to-flange interface just prior to catastrophic failure on
the T-joint.
Figure 3: Finite element model damage step 6.
An effective stress failure criteria was used to predict the
initial damage load in the T-joints. Initial T-joint damage was
defined as the point when the effective stress, σeff of the
constrained matrix at the web-to-flange interface exceeded
the neat resin failure strength, σfm of 91.0 MPa [11].
3 RESULTS
Figure 4 shows the predicted load-displacement plot under
flexural load for specimen F1. Region 1 (up to initial failure)
is modeled with no damage. The initial crack at point “a”
coincides with a matrix crack forming in the fillet region at the
web-to-flange interface and propagating to the fiber insertion
adjacent to the applied load.
1.8
(d)
FEA Predicted (kN)
1.6
(3)
1.4
(c)
Load (kN)
1.2
1.0
(2)
0.8
0.6
4 DISCUSSION
The mechanical behavior of the T-300/PR520 transverse
stitched composite T-joints under flexure loading may be
characterized by three distinct regions as indicated on the
load-displacement plot in Figure 4. In region 1, the behavior
is nearly linear elastic up to the initial damage load, showing
only a slight amount of nonlinearity near the proportional
limit. In region 2, with increased load, the behavior is again
nearly linear. Region 3 is marked by a change in slope of the
load-displacement plot leading to catastrophic failure. The
three regions of behavior are detailed in the following
paragraphs.
2.0
Load F1
Figure 5: Damage progression effective stress, step 6.
(a)
0.4
(b)
0.2
(1)
4.448
3.937
3.429
2.921
2.413
1.905
1.397
0.889
0.493
0.000
0.0
Displacem ent (m m )
Figure 4: Predicted and actual damage progression under
flexure loading.
Under initial flexure load, as represented by region 1 of the
load-displacement plot of Figure 4, the T-joint web deflects
under increased load. This has the effect of loading the fiber
insertion adjacent to the applied load in tension and the
furthermost fiber insertion in compression. As the fillet matrix
stress exceeds the PR520 neat resin tensile strength, a
crack initiates at the outer surface of the radius filler. Initial Tjoint failure may be observed as a discrete drop in the loaddisplacement record, as shown from point “a” to “b” in Figure
4. A 25 percent drop in load-displacement at initial damage
is typical under flexure loading.
REFERENCES
[1]
The extent of initial damage may be characterized by the
damage progression FEA. Based on the damage
progression model, it can be shown that in order to match
the appropriate response of the T-joint under flexure loading
(as shown at points “a” and “b” on the load-displacement plot
of Figure 4), the crack must be extended through the resinrich fillet region and along the interface to the first fiber
insertion.
Region 2 in Figure 4 is marked by nearly linear loaddisplacement and strain-load behavior. The initial damage
has the effect of redistributing additional load to the first fiber
insertion. Increased loading beyond the initial damage load,
as represented by region 2 of the load-displacement plot in
Figure 4 point “b,” causes fiber bridging and crack
propagation to the neighboring fiber insertion. The fiber
bridging behavior gives rise to increased damage tolerance
or an ability to carry additional load beyond initial failure. The
extent of damage represented by point “c” of Figure 4 may
be represented by step 6 of the damage progression FEA
shown in Figure 3. The predicted and actual loaddisplacement behavior for region 2 is shown in Figure 4.
Good agreement is shown in region 2 between experimental
and predicted results based on the extent of damage
represented by step 6 in Figure 3.
Region 3 of the load-displacement plot in Figure 4 from point
“c” to point “d” is marked by a change in slope and
subsequent loss of T-joint stiffness. Under increased load,
the fiber insertion adjacent to the applied load continuously
degrades. This behavior is represented in the FEA model
step 6 in Figure 3 by a change in fiber insertion area. As the
insertion tow area decreases, the T-joint deflection
increases. Based on the use of a fiber-degradation model to
represent region 3 in Figure 4, good agreement is shown
between the experimental and predicted load-displacement
behavior.
5 CONCLUSION
A new type of T-joint with transverse stitching using a fiber
insertion process was characterized under flexure loading for
the first time using a damage progression FEA. Crack
initiation is predicted under flexure loading when the local
matrix stress exceeds that of the neat resin tensile strength
in the fillet region of the T-joint. The flexure damage
progression FEAs showed good correlation with the
experimentally determined load-displacement through
ultimate failure. Predictive models developed herein will be
used in future parametric studies.
ACKNOWLEDGMENTS
The authors would like to acknowledge The Boeing
Company for supporting this research and Albany
international Techniweave, Inc. for the development of the
fiber insertion process.
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